If `x<0,t h e ntan^(-1)x` is equal to

Explanation

`x<0`
`=>tanx<0`
Let `tan^−1 (x)=−t`
`=>x=−tant`
Therefore,

`−sint=x/sqrt(1+x^2)`
`=>-t=sin^-1x/sqrt(1+x^2)`
Now,
`x=−tant=−tan(π−t)=tan(−π+t)`
`=>tan^-1x=-pi+tan^-1x`
`=>tan^-1x=-pi+cot^-1(1/x)`
And

`−x=tant`
`=>cost=1/sqrt(1+x^2)`
`=>t=cos^-1(1/sqrt(1+x^2))`
`=>-t=-cos^-1(1/sqrt(1+x^2))`